Stuck on CFA Example Question

[deadculture]

I was working on a practice test for Level 1 when I came across this bugger. The answer provided makes absolutely no sense to me. I honestly think they made an error. If I don’t get to the bottom of this it will really bother me. Please give it a shot and let me know. Should be very simple.
Question:
An investor examines the following rate quotes for the Brazilian real and the Australian dollar and shorts BRL 500,000.
Spot rate BRL/AUD 2.1128 BRL 1-year interest rate 4.1%
—————————————————————————————–
Forward rate BRL/AUD 2.1388 AUD 1-year interest rate 3.1%
Question:
The risk-free arbitrage profit that is available is closest to:
a) BRL6,405.
b) BRL1,344.
c) -BRL6,327
b) is the Correct answer…somehow
This is how I got my answer:
Scenario 1(invest locally) vs Scenario 2(invest abroad then convert back):
Scenario 1.
Step 1: Simply invest 500,000 BRL locally @ 4.1%
= 500,000 * 1.041 = 520,500 BRL
VS.
Scenario 2.
Step 1: Convert 500,000 BRL to AUD, @ BRL/AUD = 2.1128 (2.1128 AUD for every 1 BRL)
500,000 * 2.1128 = 1,056,400 AUD
Step 2: Invest that 1,056,400 AUD @ 3.1% for 1 year
1,056,400 * 1.031 = 1,089,148 AUD
Step 3: Convert that 1,089,148 AUD back to BRL @ BRL/AUD 2.1388 (Locked in Forward Rate)
2.1388 AUD for every 1 BRL, so 1,089,148/2.1388 = 509,233 BRL
RESULT: Scenario 2 - Scenario 1
Arbitrage Profit = 509,233 BR - 520,500 BRL = -11,267 BRL
Ergo, no arbitrage profit, you are better off keeping those BRL and investing locally
Am I missing something here?? or is it an error?
______________________________________________________________________________________________________________
This is what the answer key gave me:
Left side of equation: BRL500,000 x (1+.041) = BRL520,500
Right Side:
1
BRL500,000 x (1/2.1128AUD/BRL) = AUD236,653 <— **Why are they doing 1 over spot?**
**500,000 BRL= 1,056,400 AUD not 236,653 AUD wtf?**
Convert domestic to foreign
2
AUD236,653 x (1.031) = AUD243,989
Invest foreign @ foreign rate
3
AUD243,989 x 2.1388 = BRL521,844
Convert foreign to domestic
Arbitrage profit = BRL521,844 - BRL520,500= BRL1,344 <—-Wtf? Any ideas?
Thanks in advance!

 

[S2000magician]

First, you misunderstand CFA Institute’s exchange rate quoting convention. BRL/AUD 2.1128 means:
BRL2.1128 = AUD1.0
If he shorts BRL, he borrows BRL today. Here are the steps:

1. Borrow BRL500,000 @ 4.1% for one year.
2. Convert BRL500,000 to AUD236,653 @ BRL/AUD 2.1128.
3. Invest AUD236,653 @ 3.1% for one year.
4. Enter into a 1-year forward contract to deliver AUD243,989 @ BRL/AUD 2.1388.
5. Wait one year. Watch a movie.
6. Your AUD236,653 will have grown to AUD243,989 (= AUD236,653 × 1.031).
7. Convert AUD243,989 to BRL521,844 @ BRL/AUD 2.1388.
8. Pay off the loan for BRL520,500 (= BRL500,000 × 1.041).
9. Your net gain is BRL1,344 (= BRL521,844 − BRL520,500).

I wrote an article on this that may be of some help: http://financialexamhelp123.com/covered-interest-rate-parity-irp-pricing...

 

[studyguy18]

Obviously not my question, but just wanted to say thanks for the great and concise answer S2000magician.

 

[deadculture]

Thank you mag, very good example, in my finance class the convention was the other way around, but that wasn’t my only problem…
I will pay it forward when I get my CFA, I appreciate it!

 

[S2000magician]

My pleasure.
CFA Institute’s convention is the opposite of the norm. Welcome to the CFA curriculum.